Show the Proof¶

In [1]:

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

Out[1]:

	step type	requirements	statement
0	instantiation	1, 2, 3	, , ⊢
	: , : , :
1	reference	7	⊢
2	instantiation	4, 42, 5, 24, 6, 26, 33, 15, 16	, , ⊢
	: , : , : , : , : , :
3	instantiation	7, 8, 9	, , ⊢
	: , : , :
4	theorem		⊢
	proveit.numbers.addition.disassociation
5	theorem		⊢
	proveit.numbers.numerals.decimals.nat3
6	instantiation	10	⊢
	: , : , :
7	axiom		⊢
	proveit.logic.equality.equals_transitivity
8	instantiation	11, 42, 33, 15, 16	, , ⊢
	: , : , : , : , : , : , :
9	instantiation	12, 24, 25, 26, 13, 14, 33, 15, 16, 17^*	, , ⊢
	: , : , : , : , : , :
10	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_3_typical_eq
11	theorem		⊢
	proveit.numbers.addition.leftward_commutation
12	theorem		⊢
	proveit.numbers.addition.association
13	instantiation	30	⊢
	: , :
14	instantiation	30	⊢
	: , :
15	instantiation	40, 36, 18	⊢
	: , : , :
16	instantiation	40, 36, 19	⊢
	: , : , :
17	instantiation	20, 21, 22^*	⊢
	: , :
18	assumption		⊢
19	assumption		⊢
20	theorem		⊢
	proveit.logic.equality.equals_reversal
21	instantiation	23, 24, 25, 42, 26, 27, 28, 33, 29^*	⊢
	: , : , : , : , : , :
22	theorem		⊢
	proveit.numbers.numerals.decimals.add_1_1
23	theorem		⊢
	proveit.numbers.multiplication.distribute_through_sum
24	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
25	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
26	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
27	instantiation	30	⊢
	: , :
28	instantiation	40, 36, 31	⊢
	: , : , :
29	instantiation	32, 33	⊢
	:
30	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
31	instantiation	40, 34, 35	⊢
	: , : , :
32	theorem		⊢
	proveit.numbers.multiplication.elim_one_left
33	instantiation	40, 36, 37	⊢
	: , : , :
34	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
35	instantiation	40, 38, 39	⊢
	: , : , :
36	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
37	assumption		⊢
38	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
39	instantiation	40, 41, 42	⊢
	: , : , :
40	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
41	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
42	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
^*equality replacement requirements